We have an IO 540 Lycoming engine, and cylinder #3 doesn't work below 1900 RPM (cold to the touch; EGT and CHT are zero; no vibration). The engine is new, what could be the cause(s)?
We cannot contact the company.
If Cyl #3 is running cold it's not getting fuel, or the fuel it is getting is too lean. The Bendix RS mechanical injection system used on Lycomings has an idle mode that takes effect when the pneumatic pressure sensing system in the fuel regulator is unable to provide an accurate signal for good operation near idle.
There could be a restriction from dirt or FOD in the line going to Cyl #3 that causes a too lean mixuture in idle mode, but it's ok when off idle mode and the flow/pressure is higher. Or there is a problem within the regulator itself that is providing insufficient flow to all the cylinders, but #3 happens to be the first to get bad enough to stop working.
In any case, there is not much you can do until you can get an expert on the system to work on it for you.
Well, if it is cold and cht and egt are zero then I you're either not getting spark or fuel or air.
It's possible that the spark plugs are not firing. Clean and bench test them. Also check that the mags are timed correctly. Maybe they work but they just fire at the wrong time.
Make sure the valve train is assembled correctly. When you installed the cylinder, did the lifters and rods get put back correctly. Also, are the rockers installed correctly. I know this sounds like a stupid thing, but sometimes people make errors.
Maybe you have a stuck or broken valve. You typically notice when this happens though! Also, if it works at some RPM and not others, this is probably not the issue.
Finally, have your A&P follow Lycoming's fuel system calibration procedure to the letter (you'll need to look this up; TCM's is SID 97-3). I had a TCM IO-520 on a V35B for a few years and when we calibrated the system we saw a noticable improvement in engine performance.
Of course, check the compressions! If you're 0/80 then you may have your answer right there.
These are just a few thoughts and it's by no means a comprehensive list of possible causes.